Different definitions of e: Index

I’m doing something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on the different definitions of e that appear in Precalculus and Calculus.

Part 1: Justification for the formula for discrete compound interest

Part 2: Pedagogical thoughts on justifying the discrete compound interest formula for students.

Part 3: Application of the discrete compound interest formula as compounding becomes more frequent.

Part 4: Informal definition of e based on a limit of the compound interest formula.

Part 5: Justification for the formula for continuous compound interest.

Part 6: A second derivation of the formula for continuous compound interest by solving a differential equation.

Part 7: A formal justification of the formula from Part 4 using the definition of a derivative.

Part 8: A formal justification of the formula from Part 4 using L’Hopital’s Rule.

Part 9: A formal justification of the continuous compound interest formula as a limit of the discrete compound interest formula.

Part 10: A second formal justification of the continuous compound interest formula as a limit of the discrete compound interest formula.

Part 11: Numerical computation of e using Riemann sums and the Trapezoid Rule to approximate areas under y = 1/x.

Part 12: Numerical computation of e using \displaystyle \left(1 + \frac{1}{n} \right)^{1/n} and also Taylor series.

 

 

 

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